PROPERTIES OF A UNIVERSAL WAVE FIELD

 

(pv-1 = const.; p/v = const. = RT)

                                                         

 

Summary:  A theoretical gas ( the Chaplygin/Tangent adiabatic  gas) is currently being studied as an exotic cosmic  fluid in cosmology to help explain dark energy, dark matter and an apparent speed-up in the expansion of the universe.

 

Here we show that this exotic cosmic  fluid has isothermal as well as adiabatic motions, and so is actually a universal compressible field (UF) with unique properties.

 

These unusual properties include (1)  the  unique ability among known  fluids or gases to propagate stable waves of any strength, which also (2) uniquely  obey the simple classical  wave equation, (3) an ability to support transverse waves, which is something impossible for any other known or theoretical fluid, and which thus provides for the first time a physical basis for the existence of the electromagnetic field and of transverse  electromagnetic waves, and  for the  transfer of radiation through space at the speed of light, (4) the ability to carry gravitational waves which transfer gravitational force through space, and finally, ( 5)  it may also serves as the  basis for the transfer of quantum information through space at quasi-instantaneous  speeds.                

 

 

Contents

1. Introduction

2. Dynamics and Thermodynamics of Compressible Exotic Fluids ( Chaplygin gas and Tangent gas) with k = −1

2a. Archive Insert: Thermodynamic Properties of an Isothermal Gas Law for the Chaplygin/tangent Field

3. A Universal Field (UF)

4. A Universal Field (UF) which Supports Transverse Waves and the Transmission of Transverse Electromagnetic Waves through Space

5. A UF Which Supports the Transmission of Gravitational Force through Space

6. A UF Which Supports the Transmission of Quantum Information though Space

7. Experimental Evidence for the UF

 

 

1.  Introduction

Is There a  Universal, Cosmic, Compressible Wave Field ?

 

The concept of a universal physical entity filling all space in the cosmos and serving to transmit electromagnetic and gravitational forces between material bodies has had a long and  interesting history [1].  Although the concept existed in the ancient classical era in a pre-scientific form, it was Descartes who first formulated it scientifically.  His ‘ether’ was incompressible, so that its light waves would need to travel instantaneously. Consequently, it was not long before Fermat pointed out that experiments showed, instead, that light traveled through space at a finite speed.  Newton tended to avoid the ethereal wave medium  and preferred a particle or corpuscular  mode for transmission of light. He did believe that gravitational forces must be moving through some sort of physical entity or medium, but made ‘no hypotheses’ about what that might be.

 

However, evidence that wave motions were undoubtedly associated with light advanced under Huygens and Young restored the concept of the wave-carrying ether, and the task of  reconciling the physical properties of this hypothetical ether  with experimental reality was again taken up. The two greatest difficulties were the known finite speed of light ( 3 x 108 m/s),  and the impossibility of any conceivable fluid being able to support the transverse vibrations corresponding to light waves.

 

Maxwell’s successful, transverse electromagnetic wave theory of light ended any lingering controversy as to the transverse nature of light waves, but did little to support the ether in its problems. In fact, the elastic ether quickly became replaced by the concept of a field with a dielectric constant and a magnetic permeability.  Almost coincidentally, difficulties in attempts to use classical methods of adding velocities of material bodies to the speed of light took front and centre as the negative results  of the optical experiments of Michelson, Morley  Miller, Joos and others were evaluated. These tests failed to show the correct orbital speed of the earth around the sun using the classical theory of the flow of light waves through an ether. The experimental  variations observed when the optical interferometers were rotated through 90 degrees were only about one-tenth  as large as predicted by the classical ether theory,  and  this result eventually was interpreted as meaning that it was impossible to use light to detect any  motion at all through space. Other optical experiments such as the Fizeau Effect and the Sagnac Effect which did show large experimental effects were eventually ascribed to different causes.

 

This led to the Poincare/Fitzgerald /Lorentz / Einstein work on relative motion, and eventually  the whole idea of an ether or wave medium  which supported light waves was abandoned.  Today, when compressible flow theory has been fully developed, this abandonment appears to have perhaps been too hasty, and a recent review of the experimental evidence from the standpoint of compressible flow as opposed to the old classical incompressible flow ( with its direct addition of velocities ( c +V) and (c-V) )  is available at website www.energycompressibility.info [ Appendix A:  Compressible Flow and Results of Michelson-Morley Type Experiments].

 

In any case, the rise of quantum theory with its photon “particle” would probably have eventually abolished the old classical ether concept  even without Michelson and Morley and their successors.

 

Historically, the ether was dead. although the problems with light were not thereby resolved. Gas dynamics, high speed atmospheric science, aeronautics and other aspects of compressible flow theory were just emerging, and so the important and significant fact that compressibility might explain the observed finite speed of light never came to the fore although it was tentatively advanced as a possible help in the solution to the Michelson-Morley dilemma by Lorentz himself..  Instead, the quite radical, essentially algebraic and geometrical theory of relativity and its Lorentz invariance took over, and it has served well enough as a fairly close approximation to the experimental results.

 

The application of compressible flow theory to relativity, electromagnetism and cosmology began in the 1980’s [2, 3, 4, 5] and the new approach immediately showed numerous successful applications to problems in these fields. Now the concept is being widely applied to the problem of the observed acceleration of expansion of the cosmos by the introduction of an exotic cosmic compressible theoretical fluid based on the so- called Chaplygin gas [6 - 12].

 

We now proceed to examine more deeply the thermodynamic and wave properties of  exotic compressible fluids and their possible interactions with our physical world.  

 

 

2. Dynamics and Thermodynamics of  Exotic Compressible Fluids ( Chaplygin and Tangent gases) with k = -1)

 

Subjects:

Basic Equations of Compressible Fluid Flow

Adiabatic Equations of State for the Chaplygin gas and Tangent gas (k  = -1)

A New Isothermal Equation of State for this Exotic Fluid  ( k = -1)

 

 

 

2.1 To describe the motions of any compressible fluid, three basic equations are needed:

 

1.Euler’s classical hydrodynamic equation of motion;

 

For 1-dimensional flow this equation is

∂u/∂t + u ∂u/∂x + v ∂u/∂y +w ∂u/∂z = −(1/ρ) ∂p/∂x                                                (2.1)

where the term on the right hand side is called  the pressure gradient force.

2. The equation of continuity, or conservation of mass

∂ρ/∂t + div (ρw) = 0                                                                         (2.2)

 

3.  Equation of State relating pressure p to density ρ ( or to its reciprocal,  the specific volume v = 1/ρ)

 

(a) For real physical gases undergoing adiabatic motions ( i.e.(no heat flow, dQ = 0) the general equation of state is :

 

pvk = constant                                                                                   (2.3)

 

p/ρk = constant                                                                                 (2.3a)

 

 

and the wave speed is c2 = kpv, where k, the ratio of the specific heats (k = cp/c­v )   is the adiabatic exponent (sometimes also denoted as γ). The adiabatic exponent ratio k is also related to the number of ways n that  the energy of the system is divided as k = (n+2)/n; n = 2/(k−1).

 

(b) For isothermal motions in a real gas, the equation of state becomes

 

pv = RT  or p/ρ = RT                                                                            (2.4)

and the wave speed now is given by c2 = pv.

 

For real gases the  equations of state all lie in Quadrant I of the pressure –volume field of Figure 1.

 

 

 

 

 

 

 

         

 

 

Figure 1.   Pressure-volume  in Compressible Fluids

                 Quadrant 1: Real gases and Tangent gas (exotic)

                      Quadrant IV. :Chaplygin gas and Tangent gas (exotic gases)

 

 

One additional relation is very useful, namely the kinematic energy flow equation relating compressive wave speed c to relative flow velocity V:

 

c2 = co2 – V2/n                                                                                      (2.5)

 

where  n  ( n = 2/(k – 1)) is the number of ways the energy of the system is partitioned.  If we divide through by the square of the static wave speed co2 we get the wave speed ratio

c/co = [ 1 – V2 / n co2 ]1/2                                                                            (2.6)

which ( when n = 1 ) is formally identical to the Lorentz/Fitzgerald contraction factor of special relativity theory (Section 4).

 

For unsteady or pulsed flow, the energy equation (2.5) becomes  c2 = co2 – V2/n – 2cV/n  where the additional, or ‘pulse’  term 2cV/n is of great interest to quantum phenomena as we shall see in Section 6.

 

 

2.2 Adiabatic Equations of State for Exotic Fluids where k= −1    

 

For real gases and fluids the adiabatic exponent k in Eqs. 2.3  and 2.3a is always positive. However, if  k is, instead, taken as being a negative number then  the properties of the resulting theoretical fluid change radically. In 1901 a Russian aerodynamicist, S.A. Chaplygin [10] first proposed such a purely  theoretical, compressible fluid  - now called the Chaplygin gas and  having  k = −1 --   to help calculate  certain features of jet flow in gases. Since his theoretical gas does not actually exist in our known physical world, it has had little application, except for simplifying some calculations in aerodynamics.

 

Within the last five years, however, the cosmological problem raised by an unexplained acceleration in the expansion of the universe  has been cited by some cosmologists [6,7, 8, 9] as indicating that the Chaplygin gas may exists as an exotic universal “cosmic fluid” which is the physical seat of the so-called  ‘dark energy’ of the universe, presently calculated to comprise about 74% of the total ‘matter’ of the cosmos.

 

The Chaplygin gas [10 - 15] has the adiabatic equation of state

pv-1= p/v = p ρ =  constant, or

 

p = −Av = −A/ρ                                                                                  (2.7)

 

where p is the pressure, v = 1 /ρ  is the specific volume, ρ  is the density per unit mass of fluid  and A is a positive constant. This equation plots with negative slope, dp/dv, on the pressure-volume diagram ( Fig. 1)  and its pressure p is always negative. This negative pressure is the attractive feature for the present day cosmologists who are concerned with the apparent accelerated expansion of the universe, and the Chaplygin gas is increasingly proposed as a physically real exotic cosmic fluid to address this cosmological problem.  However, its properties are quite bizarre compared to our real world gases and the success of this innovation in rescuing general gravitation and superstring theories of gravity is problematical. The Chaplygin gas lies entirely in Quadrant IV of Figure 1.

 

A closely related exotic fluid called the  Tangent Gas has an equation of state identical to the Chaplygin gas except for the addition of a constant B which  makes its  pressure positive for values of v less than B. It may lie in either Quadrant 1 or  Quadrant IV of the pressure-specific volume diagram of Figure 4.  Its equation of state is

 

pv-1 = constant or

 

p = −Av + B = −A/ ρ +B                                                                             (2.8)

 

In this form, the relationship became very useful to aerodynamics in the 1940’s [14]. As a tangent curve to the adiabatics and isotherms for atmospheric air, the “tangent gas” provided a linear relationship between pressure and density, which, for small variations of these variables, gives a simple approximation to the more cumbersome, exact, non-linear thermodynamic equations for any compressible fluid except the UF.                

 

2.3 A New  Isothermal Equation of State for a Compressible Fkuid with  k = −1

 

A generalized  adiabatic equation of state for the fluid with  k = −1  is pvk  =constant, and so this becomes

 

p v-1 = p/v = const. = ± A, or

 

p = ± Av                                                                                         (2.9)

 

We now must choose the sign before  the positive numerical constant A,  and this will determine the slope of the equation of state in the p-v field. In the case of the Chaplygin gas ( Eq. 2.7)  the sign is chosen as negative so as to give p = −Av = −A/ρ,   and for the Tangent gas (Eq. 2.8) as  p = −Av + B = −A/ ρ +B , mainly because this makes them both agree with all real  gases in having egative slope (dp/dv)  on the p-v diagram,  and also guarantees a  positive wave speed with c2 = +(dp/dρ).

 

However, there is also no apparent reason to completely reject the alternative choice of +A for the equation of state, that is, to chose a positive slope for dp/dv. This would give the isothermal  equation of state for the fluid:  

 

p =+ Av                                                                                       (2.10)

 

 

and                                                                                 

p = +A/ρ –B                                                                               (2.10a)

 

 

These two  new isothermal curves with positive constant A are  strictly orthogonal to the adiabatic Chaplygin and Tangent gas curves. They constitute the desired  isothermal equation of state for the fluid with  k = −1,  since  p/v  =+A, and, if the positive constant A is set equal to a constant temperature + A =RT ,we would then have p/v = RT which is certainly an isothermal relationship.

 

We then have :

 

Real gases ( k ≥ 1) :  pv>1 = constant = +A is the general adiabatic equation of state

Real gas ( k = 1) :     pv+1 = constant. = +A = RT is the ‘isothermal gas’,   and is also the equation of state for any ideal gas with                   constant temperature T.

 

Exotic gases ( k = − 1) :

 

             a)  Chaplygin gas:         Adiabatic equation of state      p = −Av = −A/ρ                                    (Eq. 2.7)

                                                    Isothermal equation of state    p = Av = vRT;  p/v = RT                      (Eq. 2.10)

 

             b) Tangent Gas             Adiabatic                                p = −Av + B  = −A/ρ + B                     (Eq. 2.8)

                                                    Isothermal                              p = Av − B = vRT −  B                        (Eq. 2.10a) 

 

We now propose to treat these exotic states,  not as  separate physical entities or ‘gases’ but instead as simply  the  adiabatic and isothermal equations of state of one single, universal  compressible field ( UF) whose adiabatic exponent  is k = −1.

 

 

 


      Figure 2.  Equations of State for the Universal Field  (k = − 1; pv-1 = const.)

 

 

 

2.a (Archived Insert) May/06

 

Thermodynamic properties of an isothermal gas law for the Chaplygin/tangent field

           

            Bernard A. Powera) 

            Montreal, Quebec, Canada

            March, 2006

 

An isothermal equation of state is formulated to match the adiabatic Chaplyin/tangent gas, and it appears to be a general gas law for a  whole field whose  thermodynamic properties are very unusual.  In this field a working substance expands with cooling and contracts with heating, and both processes take place without any work being done. The 2nd Law is inapplicable.

 

The theoretical or exotic fluid known as the Chaplygin/tangent gas has an isentropic/adiabatic equation of state which has been widely studied and applied in aerodynamics and  fluid dynamics for many years.1,2,3,4,5,6  However, the adoption by cosmology of the negative pressure attribute of the Chaplygin gas as a possible solution to the observed increased expansion of the cosmos  is only recent. 7,8,9  A potential role as a universal cosmic fluid, however, would seem to merit  an examination of all aspects of this field.  

The equation of state  for the Chaplygin gas is the  linear relationship  p = − Av,  (pv-1 = −A) ; it lies in Quadrant IV of the  p-v diagram where it always has  negative pressure. The dynamically identical Tangent gas has an added constant and  is also linear, with  p = − Av  + B, ( pv-1 = −A + B] ;  in Quadrant I it has positive pressure (Fig. 1).

The Chaplygin/tangent gas can also be described by the adiabatic equation of state  pvk  = −A, where  A is a positive constant, k has the value of − 1, and where  the minus sign preceding the constant A provides a desired negative slope -dp/dv on the pressure-volume diagram.

The proposed isothermal equation of state for this field  is  p = +Av corresponding to  the adiabatic Chaplygin gas, and p = +Av –B corresponding to the adiabatic  tangent gas.   If the positive constant A is multiplied by  a constant temperature Tc, we would then have p/v = A (T)c , p = vATc, and p = vATc − B,  which provide the desired isothermal relationship, provided that  A takes on the proper dimensions. The isotherms  in pressure and volume are seen to be  strictly orthogonal to the adiabatics of the  Chaplygin and Tangent gas. (Fig. 1)

Since v = 1/ρ , these linear isothermal relationships in pressure and volume ( p = vA Tc , etc )  can also be written hyperbolically in pressure and specific density ρ as

 

pρ = AT                                                                                                        (1)

 

The ideal gas law ( pv =  RT) is hyperbolic in pressure and volume, but linear in pressure and density ( p = ρRT).  The proposed new  isothermal  equation of state for the  k = −1 field  is the reverse, being linear in pressure and volume and hyperbolic in pressure and specific density.

It would  appear  that the new relationship is not  so much just an isothermal counterpart to the Chaplygin/tangent gas,  but  rather that it plays the more fundamental role of being the general gas law of the field, with the Chaplygin and tangent cases being simply the exceptional modifications to the gas law that apply under the adiabatic condition ( dQ = 0), just as is the case with real adiabatic gases which depart exceptionally from the ideal gas law. The term  universal field ( UF) would  embrace both the isothermal and adiabatic equations  and where  “isothermal” equation we have derived would become  the basic gas law ( pρ = AT )for the whole field.

The thermodynamic properties of this UF are very unusual because of (1) the  direct proportionality  of pressure and volume, (2   a negative specific heat either at constant volume or at  constant pressure and (3)  the positive slope +dp/dv of the isotherms on the pressure-volume diagram and its effect on expansion or contraction..

 First, the isothermal pressure increases with volume expansion is  the inverse of that for the ideal gas , so that heating now accompanies contraction and cooling brings about expansion.

Second the  entropy  relationships in the UF are also unusual since we have  k = cp/cv = −1, so that either cp or cv must be negative. In the ideal gas  with  T and V as independent variables the entropy change is    ∆S = cv ln (T2/T1) + R ln(V2/V1). And with T and P as independent variables, it becomes ∆S = cp ln (T2/T1) – R ln(P2/P1)

In the UF we have dS= cv dT + (∂P∂T)v  and, from  P =AvT we have (∂P∂T)v  = Av2/2 so that we obtain the corresponding  entropy changes in the UF  as   ∆S = cv ln (T2/T1) + Av2/2 and ∆S = cp ln(T1/ T2) )  −Av2/2

(In the UF the magnitude of the reversible heat Qr needed to calculate the entropy change  ∆S  is readily visualized on the pressure volume diagram, since the Carnot cycle is then depicted simply as the rectangle formed by the appropriate linear adiabatics  and isothermals, and Qr is  the area enclosed).

Third, the positive slope  +dp/dv  of the isothermals on the pressure-volume diagram  implies  that there is no resistance to pressure/volume increases or decreases, which would therefore take place at ever increasing speed following any initial impulse.. This is analogous to an  expansion into a vacuum in the usual analysis of  an isothermal process in an ideal gas where the work pdV is then zero  In the UF in an isothermal process it would seem that this work would also necessarily approach zero. This would mean complete reversibility of all UF processes, both adiabatic ( Chaplygin/tangent) and isothermal, with no referred direction for any  physical change.  All complete cycles in the UF would appear to be isentropic. Heat would  be convertible into internal energy but not into work.. The 2nd law of thermodynamics would not apply. Clearly the properties of this unusual field should be further explored and critically evaluated.

 

 

References

 

1..  S. A. Chaplygin,  “On Gas Jets,”  Sci. Mem. Moscow Univ. Math. Phys. 21, 1 (1904).

 

2.  H.S. Tsien,  “Two-Dimensional Subsonic Flow of Compressible Fluids,” J. Aeron. Sci. 6, 399 (1939).

 

3. T.Von Karman, “Compressibility Effects in Aerodynamics,”  J. Aeron. Sci. 8, 337 (1941).

 

4. A. H. Shapiro, The Dynamics and Thermodynamics of Compressible Fluid Flow. 2 Vols.( John Wiley & Sons, New York, 1953).

5.   R. Courant and K. O. Friedrichs,  Supersonic Flow and Shock Waves. (Interscience , New York, 1948).

 

6. Horace Lamb,  Hydrodynamics. 6th ed .  ( Dover Reprint, Dover Publications Inc.  New York, 1936 ).

 

7. N.A. Bachall, J.P. Ostriker, S Perlmutter and P.J. Steinhardt. “The Cosmic triangle:    Revealing the State of the Universe,” Science,  284, 1481 (1999).

8 A. Kamenshchick, U. Moschella and V. Pasquier,  “An alternative to quintessence,”  Phys Lett. B  511, 265 (2001).

9. N. Bilic, G.B. Tupper and R.D.Viollier,  “Unification of Dark Matter and Dark Energy: The Inhomogeneous Chaplygin Gas,”  Astrophysics, astro-ph/0111325  ( 2002).

 

 

 

 

 

 

Fig. 1. Equations of State in the UF

 

 

 

 

3. A Unique, Universal Field (UF)  1 Which Can Support Stable Longitudinal and Transverse Waves of Any Amplitude

 

The evidence seems to be that instead of  there being  three separate exotic “gases”( Chaplygin gas, Tangent gas and Orthogonal or isothermal gas) that there is only a single, compressible, fluid entity or field  having the usual separate adiabatic and isothermal equations of state.

 

 

Equations of State

Kinematic Energy Equation for Relative Motion

Force in the UF

Wave Motions in the UF

Isentropic ratios of p, ρ and T in the UF

Static pressure, density and temperature values in the UF

 

 


We now explore this proposition that there  exists a single Universal  Field (UF)which has the compressible properties of  the adiabatic Chaplygin/Tangent  gas and the new isothermal orthogonal gas, and which supports stable waves obeying the classical wave equation. In succeeding Sections this will then be expanded to show that this Universal Field is also the physical entity which supports and transmits (a) light and other transverse electromagnetic waves, (b) gravitational force between masses, and  (c) transfers quantum information through space.

 

Some of its principal physical properties are summarized as follows:

3.1 Equations of State relating pressure , p, to specific density ρ ( = 1/v) and  where n =−1 and  k = (n+1)/n = −1: 

 

                      Adiabatic:    p = −Av +  B = −A/ρ +B      (Chaplygin/Tangent  gases)                                                              (3.1)

 

 Isothermal:    p= +Av  −B ;  pv = RT    (Orthogonal Gas)                                                                               (3.2)

 

 

3.2 Kinematic  Energy Equation : ( relating wave energy c2  to  kinetic or flow energy V2, and  wave speed c to relative motion  V)

 

c2 = co2 – (1/n) V2                                                                                                                                     (3.3)

and, since n = −1 we have

c2  = co2 + V2                                                                                                                                       (3.4)                                

                                                                                                                                                                    

If we divide through by the static wave speed co2 we get

c/co = [ 1 – V2 / n co2 ]1/2                                                                                                                  (3.5)

which ( when n = +1 ) is the  /Fitzgerald/Lorentz contraction factor of special relativity theory to be mentioned in Section 4.

 

 

3.3  Force in the Universal Field (UF)

 

 In the UF as in any compressible fluid the force is given by the Euler equation ( Eq. 1).in Section 2.

 

For 1-dimensional flow this equation is

∂u/∂t + u ∂u/∂x + v ∂u/∂y +w ∂u/∂z = −(1/ρ) ∂p/∂x                                                (2.1)

where the term on the right hand side is called  the pressure gradient force.

 

 

3.4 Wave Motion in the UF

 

The Universal Field  in unique in that (1) it is the only field in which the Classical Wave Equation is strictly valid and which therefore can transmit stable waves, of either condensation or rarefaction, of any amplitude, and (2) as we shall see in Section 4 it is the only fluid which can support and transmit transverse  waves.

 

In general, the adiabatic  speed of sound waves c is related to the pressure p and density  ρ by the equation

 

c2 = (dp/dρ)s                                                                                                                                        (3.6)

 

From this, the adiabatic  speed of sound c  ( i.e. no heat flow, ∆Q = 0)) in a perfect  gas is also  

 

c2 = kpv = kp/ρ =kRT                                                                                    (3.7)

 

By Eq.  3.6  a positive wave speed c, requires that  dp/dρ must  be positive.  Since  v = 1/ ρ, we see that dp/dρ and dp/dv must have opposite signs.  Real gases, and the adiabatic equation of state for the UF ( Tangent gas)  gas all  have a negative slope for dp/dv on the pv diagram and  therefore have positive adiabatic wave speeds.

 

For compressive waves, the exact wave equation, expressed in terms of the wave function ψ for amplitude, is [13]

 

Ń2 ψ  = 1/c22ψ/∂t2  ∕ [ 1 + Ńψ ](k + 1)                                                                (3.8 )

or, for one- dimensional motion in the x-direction

 

2ψ //∂x2  = [(1/c2) ∂2ψ /∂t2 ]  ∕ [ 1 +    ψ /∂x ] 1+k                                                      (3.8a)

 

This exact equation means that for real  gases ( k > 0) compressive waves are always unstable and grow with time . For very small amplitude waves, however, the term in the denominator of Eqs. 3.8 and 3.8a involving ψ /∂x  becomes approximately unity, and the equation simplifies to approximately become the classical wave equation n for very low amplitude sound waves (acoustic waves in real gases, which is

 

Ń2 ψ = (1/c2 )∂2ψ/∂t2

 

 and which has the general solution

ψ = ψ1(x – ct) + ψ2 ( x – ct)

 

In the  case of the  UF, however we see that, since k = – 1, the exponent  ( k + 1) in the denominator of Eqs. 3.8 and 3.8a  becomes  zero, thereby automatically  reducing these  equations to the simple classical wave equation, but without any of the approximation needed for real gases such as air.

 

The UF is therefore truly  unique in that it automatically becomes exact for waves of any wave amplitude, large or small  and is no longer limited to infinitesimal waves, as is the case with  real gases. The UF is  therefore unique among gases, since in all real  gases finite amplitude waves always either steepen to eventually form shocks or they  die out, and only sound waves of  infinitely low amplitude can persist as stable waves [12,13].

 

The natural representation of the general solution of the classical wave equation

 

ψ = ψ 1x – ct) + ψ 2( x + ct)

 

is on the (x,t), ‘ physical plane’  or ‘space-time’ diagram.  Figure 3 shows the characteristic lines representing two families of one-dimensional left-running and right-running waves in this’ space-time’ or ‘physical plane’[12].                

 

                         

 

Figure3. Space-time ( physical plane)  Plot of Wave Characteristic Lines (1-dimensional ) 

 

 

For isothermal motions ( i.e.  constant temperature,  ∆T = 0), we have the isothermal (Newtonian) speed of sound waves in a real perfect gas

 

c2 = pv =  p/ρ = RT ;  c = [pv]1/2 .                                                                     (3.9)

 

 

Now with our exotic gases we have


a. The Tangent ( i.e. adiabatic)  Equation of State is:          p = −Av + B                                                                                (3.10) 

 

The general adiabatic sound speed equation is c2  = kpv, therefore, in the Tangent case we must have

 

c2 =k pv = k  [−Av2 +-Bv] = +Av2 − Bv                                                              (3.11)                                                         

 

and the sound wave speed c is positive as it should be.

 

b  Our  isothermal equation of state is:     p = +Av − B

 

 The  wave speed  in an isothermal gas is given by  c2 = pv, and therefore we must have

 

c2 = pv = v[+Av − B] =  +Av2 − Bv                                                                     (3.12)

 

Therefore, since the right hand side of Eqn 2 is positive, the isothermal state also has a positive wave speed.

 

Moreover, since Eqs. 1 and 2 yield the identical result (c2 = +Av2 − Bv) then  the wave speed c is the same for both the adiabatic and isothermal states.  This agreement of the two wave speed is additional evidence that our adiabatic and isothermal equations for the  k = −1 field are correct.

 

So far we have not distinguished between longitudinal and transverse wave motions in the UF. Clearly  longitudinal waves are  supported in the UF, and, moreover, they are not restricted to low amplitude acoustic type waves as in real gases where  k is positive. However, for the case where adiabatic and isothermal motions are both  present  we shall see that transverse fluid waves are also uniquely supported in the UF (Section 4)  and that they in fact correspond to Maxwell’s electromagnetic waves. The quantization of  UF waves is also presented in Sections 4 and 5.

 

3.5  Isentropic ratios ( c, p, ρ, T)  and relative motion (V)

 

The general isentropic ratios relating  pressure, density and temperature for any gas [12] are ( using n = 2/(k−1))

 

c/co = [p/po]1/(n+2)  = [ρo/ρ]1/n =  [T/To]1/2                                                                (3.13)

 

 In the UF  where k = − 1 and t n =2/(k – 1) =  − 1,  these  isentropic ratios then become simply

 

c/co = p/po = ρo/ρ = v/vo  = [T/To]1/2                                                                                                               (3.14)

 

 

 

Similarly, the kinematic energy equation for relative motion (Eq. 3.5)  with k = − 1 and  n  = 2/(k− 1) = − 1  becomes 

 

c/co = [ 1 + (V /co)2 ]1/2                                                                      (3.15)

 

Therefore, we also have 

p/po = [1+ V2/co2 ]1/2

 

p/po   −1  = ∆p/po = [1+ V2/co2 ]1/2 − 1                                                               (3.16)

 

∆ρ/ρ = [1+ V2/co2 ]1/2 − 1                                                                           (3.16a)

 

relating pressure pulses ∆p, and corresponding density pulses ∆ρ to relative fluid  motions V in the UF, for example to oscillations of an electric charge or accelerations of a material particle.

 

The various possible types of wave motions can then be investigated by imposing (a) condensation pulses ( +∆ρ), (b) rarefaction pulses  (−∆ρ) and (c) density oscillations ( ± ∆ρ) as in Fig. 4.

 

 

 

   

Figure 4. Density Perturbations and Wave Motion in the Universal Field

 

 

Figure 5. Various Wave Motions in the UF

                         

 

3.6  Static Values of Pressure, Temperature and Density for the UF

 

In any compressible field the basic initial values of interest are often those there is no fluid flow ( V = 0). These are called the static values and are designated as po,  To  and ρo . Their numerical values remain to be determined.

 

Having shown that the Universal Field  is a unique wave medium supporting a variety of stable wave types and uniquely obeying the classical wave equation without approximation , we now proceed to show how it can also support transverse waves corresponding exactly  to Maxwell’s  transverse electromagnetic waves  which transmit light and  radiation through space. 

 

 

4,  The  Universal Field (UF)  Supports Transverse Waves Which Are fofrmally Identical to  Transverse Electromagnetic Waves in  Space

 

4.1 Real gases can only support longitudinal waves, that is waves in which  the density variations ±∆ρ are along the direction of wave propagation. Real gases cannot support transverse waves in which the density variations would be transverse to the direction of wave propagation. Its was this inability to transmit the transverse waves of light which led to the demise of the old luminiferous ether concept.  We now ask:  What is the evidence for transverse fluid waves  in  the Universal Wave Field (UF ) with its orthogonal adiabats and isotherms?

 

Subjects

Evidence for transverse fluid waves

Maxwell/s electromagnetic waves

Polarization and spin

Quantization: Photons

 

 We consider a simple pressure pulse ( ±∆p) in the UF as in Fig.6 below:

 

  

 

 

Figure 6.  A pressure pulse ( ±∆p) in the Orthogonal  Environment of the UF

 

 

The initial or static state is designated as po. When the pressure pulse ( +∆p) is imposed from outside in some way the UF must respond thermodynamically in two completely orthogonal and hence two completely isolated ways, namely, by (1) an adiabatic stable wave along the adiabat ( TG) and (2) by an isothermal stable pulse along the isotherm (OG).

 

Spatially, the pressure disturbance ( +∆p)  must propagate in the direction of the initial impulse. But, since the two components of the pulse are orthogonal, they must still remain completely independent and physically  isolated.

 

 The only way possible for this to take place is for the two mutually orthogonal components to also be transverse to the direction of propagation of the two pressure pulses.  Vectorially, this requires an axial wave vector  V in the direction of propagation ( say z)  with the two pulses orthogonally disposed  in the x-y plane. i.e. TG X  OG = V which is reminiscent of the Poynting energy vector  S  = E x B in an electromagnetic wave.

 

 

 E

 

 

 

A  wave of amplitude ψ traveling in one direction (say along the axis x)  is represented by the unidirectional  wave equation

 

dψ/dx = 1/c dψ/dt

 

4.2 Maxwell’s electromagnetic waves

 

Here, however, in the case of our adiabatic and isothermal pressure pulses  we have two coupled yet isolated unidirectional waves, and this reminds us of Maxwell’s coupled electromagnetic waves for E and B, as follows

 

dEy/dx  = (1/c) dB/dt and dBy/dx = (1/c) dH/dt

 

where c is the speed of light, E is the Electric intensity and B is the coupled magnetic intensity.

 

Maxwell’s  E and B vectors are also orthogonal to each another and transverse to the direction of positive energy propagation.

 

Therefore, we have established in outline a  two component wave system in the Universal Field (k = −1) which formally corresponds to the E and B two component orthogonal system of Maxwell for electromagnetic wave propagation through space in a continuous medium. His equations for E and B are

 

Curl E  ∂ = −(1/c) ∂B/∂t                                                                     (4.1)

 

Curl B = (1/c) ∂E/∂t                                                                       (4.1a)

 

If we now designate our Tangent gas as A ( for Adiabatic) and our Orthogonal gas as I ( for Isothermal) then our analogous wave equations would be

 

Curl A = − (1/c) ∂I/∂t                                                                      (4.2)

 

Curl I =   (1/c) ∂A/∂t                                                                   (4.2a)

 

The two systems are formally identical. Therefore, we propose that the medium in which Maxwell’s transverse electromagnetic waves travel through space  is physically identified with being a Universal  Compressible Field  (UF) having the above described thermodynamic properties for adiabatic and isothermal motions initiated in the UF by imposed pressure pulses ( presumably by accelerated motions of electric charges.) The compressibility of the UF now properly accounts on physical grounds for  the finite wave speed ( speed of light), and in addition  wave motions in this fluid medium are transverse as required by the electromagnetic observations.

 

It is possible to reduce Maxwell’s two equations UF equations to a symmetrical single wave equation

 

 2E/∂x2  = (1/c2) ∂2E/∂t2                                                                                                                          (4.3)

 

2B/∂x2  = (1/c2) ∂2B/∂t2                                                                        (4.3a)

 

 

and similarly with A and I  for our Adiabatic/Isothermal coupled wave in the UF:

 

2A/∂x2  = (1/c2) ∂2A/∂t2                                                                         (4.4)

                                                                           

2I/∂x2  = (1/c2) ∂2I/∂t2                                                                          4.4a)

 

 

This is not surprising since the UF with its k = −1 thermodynamic property is the unique  compressible fluid which automatically generates the classical wave equation ( Eqn. 10) with its stable, plane waves. The formal agreement of the UF theory with Maxwell is again striking.

Instead of taking our initial external perturbation  as a pressure pulse ( +∆p)   we should  more realistically from the physical standpoint take it to be a density condensation (s = ( ρ – ρo ) / ρo =  +∆ρ/ ρo). This will now result in a positive pressure pulse   (+∆p) appearing in the adiabatic  (TG) phase of the UF but a negative  pressure pulse ( −∆p) in the isothermal or orthogonal perturbation component (OG) . This perturbation is represented by the two orthogonal sets of arrows on the pv diagram, one corresponding to +∆p and the other set corresponding to − ∆p. As the wave progresses the two orthogonal vectors also rotate.

  S

 

Figure 5. The physical ambiguity which results from a pressure/density perturbation in the Orthogonal UF

 

An oscillating density perturbation ( ±∆ρ) then results in an axial wave vector having two mutually orthogonal copmponents (A.I.) of a density perturbation wave.   This appears to correspond formally to the Maxwell electromagnetic wave system with its two mutually orthogonal vectors for electric field intensity E and magnetic field intensity B.

 

We have thus established a case for the compressible  UF being a cosmic entity which transmits transverse electromagnetic waves through space.   A necessary next step will be to examine the UF in relation to all the other established facts as to light and other radiations. These must include the nature of electric charge, electrostatic fields, the compressed fields of moving charges and the resulting magnetic fields, etc. etc. Preliminary work has indicated that this additional reconciliation will be a complete and successful one.

 

4.3 Polarization and Spin

 

Since we are dealing here with two linked mutually orthogonal states, all the formal requirements of electromagnetic polarization and spin are automatically satisfied.  Various other  physical details remain to be examined by specialists.

 

4.4 Electromagnetic Wave Quantization: Photons and the Orthogonal State Waves

 

Perhaps a bit simplistically we could just consider each individual axial vector wave as single basic wave entity or quantum entity and then  build up more complicated energetic states by  superposition of the basic  linear waves.

 

However, the quantization can be seen on a more physical  basis if we set the  UF’s static or rest pressure poi at some small value very close to  p = 0., say at po = 6.673 x10-11 kilopascals. This at once makes the maximum allowed value of the pressure fluctuation −∆p equal to  6.67 x10-11 kpa. as well. 

 

Now we ask what happens if the initiating pressures ( density ) oscillation  is of greater amplitude then 6.67 x10-11 kpa? Energy conservation is achieved if the energy input driving the wave is divided into N quantized units all of the same maximum permitted pressure amplitude ± ∆ ρ = ± ∆p = N x const. = n x 6.673 x10-11 kpa/., where N is a positive quantum integer. This of course is just an application of the energy relation ε = Nhν in quantum radiation theory. This quantization procedure is also applied to gravitation in the succeeding section.

 

 

 

 

Figure 6. Forced quantization of large input density pulse +∆ρ by very small static pressure level po

 

 

 

4.5 Special Relativity:  The question of whether the Universal Field  proposal reintroduces a cosmic “medium” into space will also undoubtedly come up, although it is more a matter for experiment to settle rather than for theory.  In the UF all motions are physically purely relative, which is to say that  the physical effects of motion depend only on relative motion between the field and matter. In a compressible field the laws to be tested are those of compressible motion and not those of  classical incompressible motion which have heretofore always been used in evaluating the Michelson-Morley and other optical  motion experiments ..

 

The kinematic energy equation  (3.3) yields the Lorentz/Fitzgerald transformation (Eq. 3.5) but in  a more general form than special relativity, and now on physical rather than on postulation grounds. In the matter of the central problem of  special relativity, which involves the direct mathematical addition of material source velocities to the velocity of light, the addition formula from compressible theory containing the energy partition parameter n ( Eq. 3.5) must be used,  and not the failed approach of using the classical direct addition of velocities( e.g. c + V and c −V)  which led  special relativity being introduced in the first place.

 

To repeat for clarity in this matter, the new addition rule will involve  (c ±V/√n) instead of the old classical (c ± V).  From the  kinematic energy flow equation

 

c2 = co2 – (1/n) V2                                                                             (3.3)

 

 we get the ratio of wave speeds

 

c/co = [ 1 – V2 / n co2 ]1/2                                                                      (3.5)

 

which sets the correct velocity addition formula for compressible flows. We see that it involves the introduction of the thermodynamic energy partition  parameter n  ( n = 2/k – 1).    In most cases this addition of n  reduces the expected fringe shifts and oscillations changes predicted by the failed classical formula and bring them  into line with experiment.  For details see a current review of the observational data of the Michelson-Morley and later experiments at website  www.energycompressibility.info

 

The formulae of the Lorentz transformation, and hence of special relativity, are formally identical   to the above formulae for compressible flow only  in  the special case of n = +1  ( k = 1.67) , for example in  opne-dimensional flow experiments on the  apparent increase of mass with relative velocity in accelerators.  However, in general,  the value of n for any given experimental system will not be unity,  since a relative motion  experiment involves not just the wave transmitting field but its interaction with  the  motions and accelerations of matter.

 

Summary.  Maxwell’s electromagnetic field equations involve two mutually orthogonal field vectors E and B which obey the classical wave equation and form a  transverse wave propagating in space. Maxwell’s system is a complete and self-consistent theoretical structure which then agrees with the facts of experiment.  The UF  is the only known theoretical field ( k = n = −1) which can support classical wave motion without approximation, and which furthermore involves two mutually orthogonal field vectors A and I  which can form and support a transverse wave propagating in the UF through space. The two systems are formally identical, and, since Maxwell’s equations are fully verified by experiment, then the UF system is also thereby verified.

 

Finally, if the  UF can solidly establish itself as a unique, compressible fluid medium which transmits transverse electric and magnetic waves, then the question naturally arises:  Can the compressible UF also account for the unique nature of, and the spatial transmission of, the force of gravity?   This is discussed  next.. 

 

    

 

5. The UF as a Support for the Transmission of Graviational Force Through Space

 

Subjects

Exclusively attractive nature of gravitational force

Extreme weakness of gravitational force

A unique wave speed associated with gravitational and other UF waves

                                                

Gravitational Characteristics:   The principal characteristics of gravitational force to be properly  accounted for in a new theory are (1) its exclusively attractive nature for mass, (2) its extreme weakness relative to the electromagnetic force, and (3) its 1/r2 decline in strength with distance.  Newton’s formulation avoided any speculation as to the physical nature of the gravitational force and the manner of its transmission through space between material bodies. General relativity is based on the postulate of the existence of a geometrical  space-time continuum; deformations in this continuum then constitute force, which is interpreted as being a deviation from linear motion.

 

Any new, physically based theory attempting to explain the nature and behaviour of gravitation will obviously have to account for  the three physically characteristics set out above. It will not have to meet the general relativity postulates, but it will eventually have to explain why the latter theory does make successful  predictions which offer corrections to the Newtonian predictions, such as the advance in the perihelion of Mercury, and various gravitational lensing effects on light waves.

 

5.1  Exclusively attractive forces in the Universal Field

 

In any compressible fluid force is given by the Euler equation , which for  1-dimensional flow is

F = ∂u/∂t + u ∂u/∂x + v ∂u/∂y +w ∂u/∂z = −(1/ρ) ∂p/∂x                                                (5.1)

where the term on the right hand side is called  the pressure gradient force.

 

 

In any compressible fluid medium, waves set up local transient  pressure forces. Most waves in real gases and fluids are pressure oscillations (±∆p) and so they  do not exert any net directional force on a material object they encounter.  However, in the UF special types of waves can occur which can be either exclusively pressure compressions (+∆p) thereby exerting a net repulsive force on any material body in their path,  or they can be exclusively pressure rarefactions (−∆p)  which would then exert exclusively attractive force.

Consider Figure 6 where a condensation pressure pulse (+∆ρ; +∆ρ)  imposed on the initial static pressure po  in the UF will produce a rarefaction pressure pulse  (−∆ρ)  in the isothermal mode of response. Consequently, a source of pressure condensations will produce a train of isothermal pressure pulses as a response in the UF, and these pulse will travel spherically outwards through space.

When these rarefaction waves eventually impact a material body (mass)  they will exert a net attractive force on it. This mechanism therefore in simple outline is formally equivalent to the force of gravity being produced by a rarefaction pressure gradient force.

 

                                       

 

Figure 7.  Positive density pulse ( +∆ρ)  of any magnitude produces a quantized gravitational rarefaction pulse (−∆pg )  of constant magnitude pg =6.67 x 10-11 kilopascals

 

 

5.2  Extreme Weakness of the Gravitational Force and the Universal Field

 

The three main forces in nature are the strong nuclear force, the electromagnetic force and the gravitational force. The nuclear force is much  the strongest. The electromagnetic force is about 1/137 th of the nuclear force.  The force of gravity, however, is incredibly weaker that the other two, being only about   10-40  th of the strength of the electromagnetic force. Thus we have

 

Fs / Fe/m = 1/137 ; and Fg / Fe/m = 10-40

 

We have shown above that a wave train exclusively made up of pressure rarefactions would explain the attractive nature of gravity. Now we must explain how these rarefaction waves can all be so extremely weak.

 

Consider a positive density pulse (+ ∆ρ) imposed on the UF at some point O (Fig.6).  Adiabatically this will result in a pressure increment  (+∆p) , but in the isothermal mode this will give a pressure rarefaction  (−∆p).

 

We  must now consider whether a sufficiently large  negative  pressure pulse  (−∆p) can transmit in the isothermal mode  right through the p = 0 point of expansion and on into the negative pressure region of Quadrant IV. It appears that it cannot, because of the fact that a negative pressure will entail a negative temperature, and quantum theory and experiments show  that temperature of opposite sign are not equal in magnitude [a, b, c] Thus the isothermal condition will be discontinuous on the v=axis at the p = 0 point.   Physically this appears to require that the negative pressure pulse must terminate at this point. The consequence then is that all negative isothermal pressure  pulses will be of the same amplitude,

 

(−∆p) isothermal = ( po – 0)  = pg – 0 =  constant  = 6.67 x 10-11  kilopascals.

 

 

Therefore, if the initial pressure/density  perturbation is inserted into the UF at its static pressure pg = 6.67 x 10-11 kpa,  then the induced negative isothermal pressure rarefaction (−∆p ) will be (a) extremely weak  and always of the same amplitude of 6.67 x 10-11 kpa. no matter what the amplitude of the initiating positive density pulse (+ ∆ρ).

 

Again, we have Fg = − v dp/dx = − 1/ ρ dp/dx . Therefore,  for unit mass at unit distance we have Fg = − ∆p = G = 6.673 x 10-11.  Thus the basic UF static pressure  po  seems to correspond numerically to G, the gravitational constant, as we have just postulated  (po = 6.673 x10-11 kilopascals).

 

On this physical model, gravitational force is carried through space isothermally by a train of rarefaction pressure pulses (−∆p), all physically constrained to have  the same invariant  amplitude regardless of the amplitude of the initiating / density pulse (+ ∆ρ).  

Now the gravitational force is known to be around  10-40 th of the strength of the electromagnetic force when the latter is set at  unity.  Then to  show that our gravitational formulation gives  the required weakness for the gravitational force, consider Newton’s force formula

Fig =( G m1 m2) / r2                                                                                                                              (5.2)

and the Euler pressure gradient force

Fp.g = −1/ρ (dp/dx) = −v (dp/dx)                                                               (5.3)

 

If we now take dp = lGl and, realizing that the equation is for unit mass ( m = 1) , we get (at unit distance  dx = 1)  the force

 

Fg  = − (1) 6.67 x 10-11  Newtons  on a unit mass. For the force on a single  proton  ( mass = 10-28 kg)  we would then  have

 

Fg  = 10-28 [ 6.67 x 10-11] = 6.67 x 10-39 Newtons, which is the order of magnitude required..

 

 

 

While this is only a rough calculation, it shows that the theory yields the required general magnitude for the strength of the gravitational force.

 

5.3  A Unique Wave Speed Assciated with  Gravitational Waves

 

In general, in the UF the wave speed, given by c2 =(3 x 108)2  = ∆p /∆ρ holds, and the wave speed c is the speed of light in space . However, consider what happens when in the generation of a gravitational wave pulse as just  described above, the reduction in p in the isothermal mode approaches the  zero pressure point.  At this point, if the wave pressure action then cannot continue on into negative values ofs p in Quadrant IV as required by the magnitude of the initiating positive pressure pulse , then we have  the UF fluid approaching a state where v = 1/ ρ = constant and so any additional ∆ρ needed must become zero. But  then   the gravitational wave speed must approach infinity since  c2  = dp/ 0 must then equal infinity.

 

As to the probable magnitude of this new gravitational pulse wave speed we propose the following:   The ratio of the gravitational constant to that of the Planck constant is

G/h = 1.04 x 10 23 = constant                                                                        (5.4)

 

If  mass is taken as dimensionless ( as we do everywhere in this theory on the grounds that mass is a condensation of  energies and so can be consider a ratio of energy before and after elementary  particle formation )  then the dimensions of the ratio  G/h  are  those of velocity or speed  [l t-1].

 

It thus seems possible that the ‘reflection’ of the positive pressure  waves of Quadrant I at the p = 0 boundary or discontinuity may generate an additional transient, extremely fast UF wave as well as propagating  the basic electromagnetic or gravitational pulses that it reflects and sustains.. This new wave seems more likely to relate to the spread of quantum information through space rather than to the transfer of energy.

 

In summary, we have exclusively attractive gravitational waves traveling as the speed of light speed of light, but at the same time as each wavelet reaches the zero pressure point ut emits a secondary wave which spreads spherically at quasi-instantaneous speed.

For a variety of reasons it is reasonable to associate this secondary quasi-instantaneous pulse radiation with quantum wave information spread.

 

 

Summary. We have shown that the UF can support and transmit stable  rarefaction waves which (1) exert exclusively attractive force on masses and (2) have the necessary extreme weakness. This meets the general requirements for them being gravitational  waves and for the UF therefore being the physical seat of universal gravitational force.

 

There are, of course, many other aspects of gravitation we have not considered here These also will have to be considered in light of the  theory, but they are not essential for this general presentation.

 

 

6. The UF as a Support for the Transmission of Quantum Information  Through Space

 

Subjects

Compressibility and Quantum Mechanics

Quantum Wave Function

Normalized Quantum Wave Function

The Extra Energy term 2cV and Fundamental Quantum Relationships

Mass Ratios of the Elementary Particles of Matter

Quantum Wave Speed, Entanglement and Collapse of the Wave Function Problem

 

 

While this subject has not yet been studied in great detail, there are some  aspects which already indicate that compressible flow and the UF concept are intimately related  to quantum phenomena, just as has been shown above for electromagnetism and gravitation.

The standard model of quantum physics is one of the most remarkable achievements of science.  It explains an enormous range of nuclear and atomic phenomena to a very high degree of accuracy, and is logically quite consistent.  Yet, for all its success, it has some serious deficiencies.

For example, while it is very successful in describing many aspects of particle creations, annihilations and interactions, it still has no predictive power to specify the values of the observed masses, and the mass-ratios of the elementary particles – the experimentally determined values of these masses must still be put into the theory by hand.  Again, it requires the arbitrary introduction of various fundamental constants, such as the speed of light c, and the fine structure constant of the atom α, which are essential for its calculations, but for whose physical existence or numerical value it has no explanation whatsoever.  Again, quantum physics is still essentially unrelated to classical mechanics, and although it can be related to electromagnetic theory through quantum electrodynamics, this is so only for the cases of the electron – the phenomena of the nucleus of the atom are as yet still essentially unrelated to the rest of physical science in the standard model of quantum theory.  Perhaps most seriously it has no explanation for the physical nature of the basic quantum wave function, nor for the transfer through space of quantum information, nor for the famous problem of the ‘collapse of the wave function’, nor for the wave/particle duality of matter. Yet again, quantum physics has little relationship to relativity, gravitation and cosmology.

Here we shall touch on only a few key aspects  as an indication of the relevance of the compressible  field (UF)  theory to quantum physics.                

6.1 Compressibility and Quantum Mechanics

We shall take the position that all quantum phenomena are basically compressible energy flow manifestations. The basic energy form ( variously to be called a characteristic, ray, wave pulse, wavelet, etc.) is the quantum wave function ψ which refers to a single, compressible, enray pulse or wavelet.

More complex waves ( elementary particles, etc. ) are built up from the linear enray ψ by superposition in a irreversible  shockwave compression event.

 

1. The unsteady flow ( wave pulse) energy equation is, as shown above 

 

c2 = co2 – (1/n) V2 – 2cV/n                                                                   (6.1)

 

where the extra energy term 2cV/n is the result of the pulse or acceleration of relative motion. For the electromagnetic case tthis could refer to the energy of the acceleration or oscillation of a charge which generates the electromagnetic waves.  All the other basic quantum relations such as the  de Broglie wave /particle equation  p = h/λ, the  Heisenberg uncertainty relationship, the quantum operators for position and momentum and so on, can also be derived  from this 2cV or ‘extra energy “ term. ( see  below)

6.2 Basic Quantum Wave

The wave function  ψ is the linear, ‘characteristic’, or ‘ray’ solution, of the hyperbolic, linearised, approximate differential equation called the classical wave equation

Ń2ψ = 1/c2  2ψ/∂t2 ;         2ψ/∂x2 = 1/c2  2ψ/∂t2                                                                             (6.2)

Therefore, the basic formula for the characteristic or ray is as follows:

Ψ = c ± V

This may also be complex, as                                              Ψ = c ± iV  

 

6.3 Quantum Wave Function

ψ = c ± V                                                                                     (6.3)

Here, V is the relative velocity and may be set to zero, making c = co in the ‘at rest’ coordinate system chosen. (cf. Sects. 2.8; 5.2). For an energy flow, co is 3 x 108m/s.

In general, ψ is complex, and we then have

ψ = c ± iV                                                                                      (6.4)

and                                                                                     ψ2 = c2 – 2icV  +V2

The physical nature of the quantum wave function is thus the relative flow velocity  V ( or particle  momentum, mV = p)  plus the wave velocity c (or wave momentum, mc).

This still leaves open the question of  the physical nature of the wave and the wave field, which however have been dealt with above where the classical waves of the Universal Field (UF) ( n and k both equal to –1) were  considered both for electromagnetism and for gravitation.

6.4 Normalized Quantum Wave Function

From the kinematic energy flow equation  (c/co)2 = 1 – 1/n (V/co)2,   we have the normalized wave function

  ΨN = c/co + i V/co;        ψ*N = c/co – i V/co                                                                                              (6.5) 

For small V, this reduces to ψN ≈ c/co.

This  wave speed ratio c/co relatesof course,  to  all the isentropic, thermodynamic ratios    p/po, ρ/ρo, T/To  as

c/co = [p/p­o­]1/(n+2) = [ρ/ρo]1/n = [T/To ]1/2

 

For the UF where k = – 1 = n, we have                  

c/co = p/po = ρo/ρ = [T/To]1/2                                                                      6.6)

The Fitzgerald/Lorentz contraction factor in the general case is now c/co = [ 1 – (1/n) (V/co)2 ]1/2 . For the UF where n itself is negative, this has the minus  sign reversed to become 

c/co = [ 1 + V2 /co2 ]1/2                                                                           (6.7)

a new Lorentz relationship which requires special study.

 

6.5 The ‘Extra Energy’ Term, 2cV yields the Following Fundamental Quantum Relationships:

The unsteady energy equation

c2 = co2 – (1/n) V2 – 2cV/n                                                                   (6.8)

 

contains a wave pulse energy term 2cv. Here we show that this then yields the fundamental quantum relationships as follows

 

a)  Planck’s Constant  h

For n = 1, if cV = constant energy for each  waves, then cV/υ = constant energy per cycle or pulse:

cV/υ = h

cV = hυ = hω/2π = ħω = ευ                                                                                                                (6.9)

For the complex case,

cV/υ = ħ/I = -iħ

 

b)   De Broglie Wave /Particle Equation

cV/υ = h

But c/υ =  λ;  V(m) = p (momentum), so

λp = h, or

p = h/λ                                                                                     (6.10)

 

c)   Lagrangian Function, L

L = 2cV 

 

d)   Quantum Wave Function Operators :

1) Hamiltonian Energy Operator

cV= hυ = -ħω = ε                                                                          (6.11)

icV = -iħω

But

iω = ∂../∂t, and so cV = h/I ∂../∂t = +iħ∂../∂t = Hop

which is the Hamiltonian energy operator.

( To ensure correct dimensions, it must be applied to the normalized quantum function ψN).

2) Momentum

cv = hυ = +hω = ε

V = (1/c))ħω, or (m)V = p = (m)(1/c)ħω

Multiplying by i, we have:         

 (m)iV = (m)(1/c) iħω

= (m)(1/c) ħ ∂../∂t

So, we have

(m) V = p = (m)(1/c) iħ ∂../∂t

But,

I1/c) ∂../∂t = ∂../∂x, and so

(m)V = p = -iħ∂../∂x = pop                                                                                                                (6.12)

which is the quantum wave operator, ( to ensure correct dimensions, it must be applied to the normalized quantum function ψN).

 

e)   Heisenberg Uncertainty Principle             

cV = hυ;  cv/υ = h

λV = h

But λ = Δx and V(m) = Δp, so

Δx . Δp ≥ (m) h                                                                              (6.13)

which is the Heisenberg uncertainty principle.

 

6.6 MASS RATIOS OF ELEMENTARY PARTICLES

It has been proposed that all elementary particles of matter (with the possible exception of the neutrino) are condensed energy forms. The forms are given in terms of a simple, integral number n ( n = degrees of freedom of the compressible energy flow):

Baryons and Heavy Mesons

For the baryons and heavy mesons the energy condensation that produces the mass is postulated to take place via the strong shock option [  ] and is proportional to the shock strength given by = [n+1]1/2

mb/mq = Vmax/c* = [n+1]1/2                                                                                                                       (6.14)

 

mb is the mass of any baryon particle, mq is a quark mass, Vmax = co n1/2 is the escape speed to a vacuum; that is, it is the maximum possible relative flow velocity in an energy flow for a given value of n, the number of degrees of freedom of the energy form,   This is a non-isentropic relationship, and it corresponds physically to the maximum possible strong shock.

Experimental evidence for this new baryon mass ratio formula is given in the following Table :

 

Experimental Verification of the Mass Ratio for Baryons and Heavy Mesons

--------------------------------------------------------------------------------------------    

n     n +1     [n+1]1/2    Particle         Mass (mb)        Ratio to

                                                      (MeV)            quark mass

0     1             1          quark (ud)         310 MeV          1

                                             (s)          505

1   

2     3             1.73      eta (η)                548.8               1.73      

3

4

5     6             2.45       rho (ρ)               776                 2.45

6

7

8     9             3          proton (p)            938.28          3.03  (1)

                                  neutron (n)           939.57         3.03

                                   Λ  (uds)             1115.6          2.97  (2)  

                                    Ξo (uss)             1314.19        2.99  (3)

9   10           3.16          Σ+  (uus)            1189.36        3.17  (2)

10   11         3.32          Ω-  (sss)             1672.2         3.31  (4)

Note: Average quark mass is 310 MeV; (2) Average quark mass is (u + d+ s)/3 = 375 MeV  (B) Average quark mass is (u+s+s)/3 = 440 MeV; (4) Average quark mass is 505 Mev.

Therefore, Equation 21 is verified to within about 1%.

Note:

For the UF with k = − 1 = n,  shocks are impossible, since V can approach but never equal c [  ] and the Mach number M = V/c never reaches or exceeds unity, as required for condensation shock formation . Also, we see that in the UF   [ n + 1]1/2  becomes zero, again confirming that no mass condensation of flow energy can take place in the  UF. Thus, the origin of the energy condensation which is our  postulated origin for the emergence of mass takes place entirely in World A where n is positive.

 

Leptons, Pion and Kaon

We form  the ration of the  mass of each lepton mL to the mass of the electron me  as          

mL/me-  =  k/α2 = [(n+2)/n]/α2 = {(n+2)/n] x 137                                                 (6.15)

where α = 1/11.703 is the fine structure constant, and k is the adiabatic exponent or ratio of specific heats, k = cp/cv = [(n+2)/n]. Because of the presence of k, this formula for the mass of the leptons is a thermodynamic and quasi-isentropic one.

The leptons are formed via the weak shock option.

The experimental evidence for the lepton mass ratio formula is given in Table below.

 

Lepton Mass ratios

n     k = (n+2)/n       Particle                  Mass               Ratio        Ratio

                                                              (MeV)              to           x 1/137

                                                                                     Electron

1/3           7              Kaon  K±               493.67            966.32          7.05

2              2              Pion π±                  139.57            273.15          1.99

4              1.5           Muon μ                  105.66            206.77          1.51

-                -             Electron                 0.511              1

 

Clearly, k ≈ ml/me (1/137), supporting Equation (22).

 

6.7 Quantum Wave Speed, Entanglement and Quasi- instantaneous Collapse of the Wave Function Problem

 

A examination of these quantum subjects indicates that a quasi-instantaneous transfer of quantum information would  remove many of the difficulties and some so-called quantum weirdness, including action at a distance problems.  It is natural then to  propose some  connection between the  quasi-instantaneous secondary  wave pulses we have discussed at the p = 0 discontinuityand which arise witrh all UF waves  if we set po the static  pressure at 6.673 x 10-11 , that is to say so near to the zero pressure point that all quantum wave oscillations automatically must reach the zero pressure point and be reflected and quantized as we have described above.

 

The possibility of a secondary wave of quasi- instantaneous speed being generated then emerges. This secondary, quasi instantaneous wave is proposed as a quantum information wave. It appears suitable for the transfer  of information at superluminal but not quite instantaneous speeds, and so able to deal with the quantum theory problems such as those  associated with action at a distance, quantum entanglement  and collapse of the wave function. and others..  

 

SUMMARY:  We have been able to  related the  fundamental quantum relationships to a single energy pulse term 2cV/n. in compressible flow theory.

We have, in effect, quantized the various energy ‘fields’ represented by 2cV/n for various values of n, by equating them to the ‘time-like’ condition set by the frequency υ in the quantum equation hυ = 2cV/n.

(Note that these equations, as is usual in compressible flow theory, are for ‘specific’ energy, that is, for  unit mass flow. For a definite particle, the numerical value of the mass is to be inserted --  the dimensions of the equations being  not thereby changed, since in our system, mass (m) is dimensionless. Thus, for the photon, we have hυ = mγ cV, where mγ is the relativistic mass of the photon. In terms of the photon momentum, we have

                                                                                    hυ = (m)cV = cp                                                                             (6.16)

which is the de Broglie equation for the photon.

 

Other fundamental difficulties with quantum  theory may also be removed by the introduction of the new  quasi-instantaneous speed for the transfer of quantum information through space..

 

7. Experimental Evidence for the Existence of the Universal Field

 

The above Sections have presented mostly theoretical evidence for the reality of the UF.

 

Naturally, verification of the theory will also require experimental evidence.  . The mass- ratio evidence in Section 6 is one  such set of experimental evidence. Another is the well established  optical shifts related to relative motion and accelerations of the Michelson-Morley, Fizeau and Sagnac type experiments Here, Lorentz himself was of the opinion that any optical effect whatever, such as a fringe shift  of any magnitude   constituted  disproof of special relativity and he quoted Einstein to back  up his opinion.

 

A new experimental approach emerges as a consequence of the new orthogonal isothermal equation of state. This isothermal state    requires a flow of heat  (∆Q) to accompany any UF wave activity. Some of this heat may possibly flow to the UF from  our  real physical world A, in which case temperature fluctuations should in principle be detectible. Preliminary, but quite extensive, experiments carried out nearly two decades ago did detect temperature fluctuations apparently linked to the inertial forces accompanying mass acceleration. These previously inexplicable findings are currently being re-examined in the light of the new UF wave theory.

 

References

 

1,  E.T Whittaker, History of the Theories of the Aether and Electricity,  2 vol., 2nd ed. London 1951.

 

2. Bernard A. Power,  Shock Waves in a Photon Gas. Contr. Paper No. 203, American Association for the Advancement of Science, Ann. Meeting, Toronto, Jan. 1981.

 

3.-----------------------,  NASA Proposal: Control No. K- 2453;  Date:, 03-31-80. Implications of a Photon Shock Wave Effect for                                      the Fizeau Experiment on the Velocity of Light in a Moving Medium.

4. -----------------------, Unification of Forces and Particle Production at an Oblique Radiation Shock Front. Contr. Paper N0. 462. American Association  for the Advancement of Science, Ann. Meeting,  Washington, D.C., Jan 1982.

5.  ----------------------, Baryon Mass-ratios and Degrees of Freedom in a Compressible Radiation Flow.  Contr. Paper No. 505. American Association for the Advancement of Science, Annual Meeting, Detroit, May 1983.

 

6. A. Kamenshchick, U.  Moschella, and V.Pasquier, Phys. Lett. B 511 (2001) 265-268.

7. N. Bilic, G.B. Tupper and R.D.Viollier.  Unification of Dark Matter and Dark Energy: the Inhomogeneous Chaplygin Gas.  Astrophysics, astro-ph/0111325,  2002.

8. P.P. Avelino, L.M.G. Beca, J.P.M de Carvalho, C.J.A.P. Martins and P.Pinto. Alternatives to quintessence model building. Phys. Rev. D.67 023511,  2003.

 

9. N. A. Bachall,  J.P. Ostriker, S. Perlmutter, P. J. Steinhatrdt, Science, 284 ( 1999) 1481.

 

10.  S. Chaplygin, Sci. Mem.,  Moscow Univ. Math. Phys. 21 (1904) 1.

 

11.  H.-S. Tsien,  J. Aeron. Sci. 6 (1939) 399.

 

12. T. von Karman,  J. Aeron. Sci. 8 (1941) 337.

 

13. Horace Lamb,  Hydrodynamics. 6th ed   (1936) Dover Reprint,Dover Publications Inc.  New York.

 

14. A. H. Shapiro, The Dynamics and Thermodynamics of Compressible Fluid Flow. 2 Vols. J. Wiley & Sons, New York, 1953.

15.   R. Courant and K. O. Friedrichs,  Supersonic Flow and Shock Waves. Interscience , New York, 1948.

 

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  Copyright 2005 Bernard A. Power [Consulting meteorologist (ret.)]